Logarithmic Sobolev Inequalities: A review on stability and instability results
Brigati G, Dolbeault J, Simonov N. 2026. Logarithmic Sobolev Inequalities: A review on stability and instability results. La Matematica. 5, 5.
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Author
Brigati, GiovanniISTA;
Dolbeault, Jean;
Simonov, Nikita
Corresponding author has ISTA affiliation
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Abstract
In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the Lebesgue and the Gaussian measures, and discuss their differences in terms of moments and stability. We give new and direct proofs, as well as examples and discuss the stability of a logarithmic uncertainty principle. Although we do not cover all aspects of the topic, we hope to contribute to establishing the state of the art.
Publishing Year
Date Published
2026-01-08
Journal Title
La Matematica
Publisher
Springer Nature
Acknowledgement
This work has been supported by the Project Conviviality (ANR-23-CE40–0003) of the French National Research Agency. G.B. has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. The authors thank a referee for a careful reading and suggestions which result in a significant improvement of the manuscript. Open access funding provided by Institute of Science and Technology (IST Austria). The work of GB has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. This work has been supported by the Project Conviviality (ANR-23-CE40–0003) of the French National Research Agency.
Volume
5
Article Number
5
ISSN
IST-REx-ID
Cite this
Brigati G, Dolbeault J, Simonov N. Logarithmic Sobolev Inequalities: A review on stability and instability results. La Matematica. 2026;5. doi:10.1007/s44007-025-00180-y
Brigati, G., Dolbeault, J., & Simonov, N. (2026). Logarithmic Sobolev Inequalities: A review on stability and instability results. La Matematica. Springer Nature. https://doi.org/10.1007/s44007-025-00180-y
Brigati, Giovanni, Jean Dolbeault, and Nikita Simonov. “Logarithmic Sobolev Inequalities: A Review on Stability and Instability Results.” La Matematica. Springer Nature, 2026. https://doi.org/10.1007/s44007-025-00180-y.
G. Brigati, J. Dolbeault, and N. Simonov, “Logarithmic Sobolev Inequalities: A review on stability and instability results,” La Matematica, vol. 5. Springer Nature, 2026.
Brigati G, Dolbeault J, Simonov N. 2026. Logarithmic Sobolev Inequalities: A review on stability and instability results. La Matematica. 5, 5.
Brigati, Giovanni, et al. “Logarithmic Sobolev Inequalities: A Review on Stability and Instability Results.” La Matematica, vol. 5, 5, Springer Nature, 2026, doi:10.1007/s44007-025-00180-y.
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